#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
#define rep(i,a,b) for(int i = a; i < (b); i++)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#define PB push_back
#define FS first
#define SD second
template<class A, class B> void cmx(A& x, B y) {x=max<A>(x, y);}
template<class A, class B> void cmn(A& x, B y) {x=min<A>(x, y);}
typedef pair<int, int> pii;
typedef vector<int> vi;
int a[500005],b[500005];
signed main() {
    cin.tie(0)->sync_with_stdio(0); cin.exceptions(cin.failbit);
    int T;
    cin>>T;
    while(T--){
        int n;
        cin>>n;
        for(int i=1;i<=n;i++) cin>>a[i];
        for(int i=1;i<=n;i++) cin>>b[i];
        int suma=0,sumb=0;
        for(int i=1;i<=n;i++) suma+=a[i];
        for(int i=1;i<=n;i++) sumb+=b[i];
        if(suma<sumb) a[1]+=sumb-suma;
        else b[1]+=suma-sumb;
        int tot=max(suma,sumb);
        int l=0,r=tot;
        while(l<r){
            int mid=(l+r+1)>>1;
            vector <pair<int,int>> va,vb;
            for(int i=n,ra=mid;i&&ra;i--){
                if(!a[i]) continue;
                if(a[i]>=ra){
                    va.push_back({i,ra});
                    break;
                }
                else va.push_back({i,a[i]}),ra-=a[i];
            }
            for(int i=n,rb=mid;i&&rb;i--){
                if(!b[i]) continue;
                if(b[i]>=rb){
                    vb.push_back({i,rb});
                    break;
                }
                else vb.push_back({i,b[i]}),rb-=b[i];
            }
            sort(va.begin(),va.end());
            sort(vb.begin(),vb.end(),greater<pair<int,int>>());
            int pa=0,pb=0,mx=0,fl=1;
            while(pa<va.size()&&pb<vb.size()){
                int ra=va[pa].second,rb=vb[pb].second,mn=min(ra,rb);
                va[pa].second-=mn,vb[pb].second-=mn;
                if(va[pa].first+vb[pb].first-2<n-1) fl=0;
                mx=max(mx,va[pa].first+vb[pb].first);
                if(va[pa].second==0) pa++;
                if(vb[pb].second==0) pb++;
            }
            if(fl&&mx-2>=n){
                l=mid;
            }
            else r=mid-1;
        }
        cout<<l<<'\n';
    }
}